The absorption of light per unit length in a medium is usually quantified by the absorption coefficient α, also known as the attenuation coefficient (not entirely correct) and the extinction coefficient. For the shorter propagation length z, the total absorption is small, and the absorbed power of the incident power Pin is approximately α*z*Pin, and the total transmittance is approximately 1 − α*z. For longer propagation lengths, the transmittance is exp(-α*z), assuming that other processes that result in the scattering or reflection of light do not occur.
Note that the absorption coefficient of the field amplitude is sometimes used instead of the optical power or intensity. These coefficients are two times smaller than the corresponding intensity absorption coefficients, since the intensity is proportional to the square of the amplitude of the field.
In some cases, people use a decimal absorption coefficient that is less than ln10, so the absorption rate is simply that coefficient multiplied by the length of the optical path.
Note that the exponential decay of light intensity may come not only from absorption, but also from reflection – this can be observed, for example, for metals. Therefore, the exponential decay coefficient should not be referred to as the absorption coefficient.
If the absorption is caused by the absorption of atoms or ions (e.g., doped ions in some transparent glass or crystalline materials), the absorption coefficient is the product of the doping density (in m-3) and the absorption cross section (in m2) at the relevant optical wavelength.
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